The exotic Galilei group and the "Peierls substitution"

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dc.creatorDuval, C.
dc.creatorHorváthy, P. A.
dc.date2000-02-28
dc.date2000-03-14
dc.date.accessioned2026-07-07T10:34:01Z
dc.date.available2026-07-07T10:34:01Z
dc.descriptionTaking advantage of the two-parameter central extension of the planar Galilei group, we construct a non relativistic particle model in the plane. Owing to the extra structure, the coordinates do not commute. Our model can be viewed as the non-relativistic counterpart of the relativistic anyon considered before by Jackiw and Nair. For a particle moving in a magnetic field perpendicular to the plane, the two parameters combine with the magnetic field to provide an effective mass. For vanishing effective mass the phase space admits a two-dimensional reduction, which represents the condensation to collective ``Hall'' motions and justifies the rule called ``Peierls substitution''. Quantization yields the wave functions proposed by Laughlin to describe the Fractional Quantum Hall Effect.
dc.descriptionRevised version, to appear in Phys. Lett. B. Souriau's scheme and its relation of with the Faddeev-Jackiw hamiltonian reduction is explained. 11 pages, LaTex, no figures
dc.identifierhttps://arxiv.org/abs/hep-th/0002233
dc.identifierhttp://arxiv.org/abs/hep-th/0002233
dc.identifierPhys.Lett.B479:284-290,2000
dc.identifierdoi:10.1016/S0370-2693(00)00341-5
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/179333
dc.subjectHigh Energy Physics - Theory
dc.subjectCondensed Matter
dc.subjectMathematical Physics
dc.titleThe exotic Galilei group and the "Peierls substitution"
dc.typetext

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